解：?$(1)\frac {sin 30°}{cos 30°}=\frac 12÷\frac {\sqrt 3}2=\frac {\sqrt 3}3=tan 30°$?
對于任意銳角α，都有?$\frac {sin α}{cosα}=tan α$?
理由：如圖，?$sin α=\frac ac，$??$cos α=\frac bc，$??$tan α=\frac ab$?
∴?$\frac {sin α}{cos α}=\frac ac÷\frac bc=\frac ab=tan α$?
?$(2)①cos^2 45°+sin^2 45°=(\frac {\sqrt 2}2)^2+(\frac {\sqrt 2}2)^2=\frac 12+\frac 12=1$?
?$②cos^2 60°+sin^2 60°=(\frac 12)^2+(\frac {\sqrt 3}2)^2=\frac 14+\frac 34=1$?
發(fā)現(xiàn)：對于任意銳角α，都有?$cos^2α+sin^2α=1$?
理由：如圖，?$sinα=\frac ac，$??$cosα=\frac bc$?
?$cos^2 α+sin^2 α=(\frac bc)^2+(\frac ac)^2=\frac {a^2+b^2}{c^2}=\frac {c^2}{c^2}=1$?
